Two-particle oscillator intrinsic density matrices in the isospin formalism

Full text: The ab initio no-core nuclear shell-model calculations are plagued with a number of serious problems of long series expansion of exact wave function in shell model ones. In the light of ever-increasing model space size, it is necessary to simplify shell model states classification and formation algorithms. Moreover the approach based on using of wave functions for many particle system description is not the simplest one. The only quantities really needed for calculation of identical particle systems are intrinsic density matrices. In order to simplify shell-model calculations, we propose to use the set of quantum numbers containing only momentum, parity, isospin and one additional integer quantum number responsible for unambiguous enumeration of the antisymmetric states. On this basis we developed simple and effective procedures for calculation of all quantities related with kinematical part of the problem under consideration. The first procedure is the calculation of the one-particle and two-particle coefficients of fractional parentage (CFP's) for a single j-orbit with isospin. The CFP's are defined as the coefficients for the expansion of the antisymmetric A-particle wave function in terms of a complete set of vector-coupled parent-state wave functions with a lower degree of antisymmetry. The procedure for spurious state elimination is based on projecting out the unexcited centre-of-mass subspace by diagonalizing centre-of-mass Hamiltonian matrix in the basis of the antisymmetric A-particle oscillator functions with singled-out dependence on intrinsic coordinates of two last particles. An arbitrary number of oscillator quanta E can be involved. The third procedure is the calculation of two-particle oscillator intrinsic density matrices defined as two-particle density matrices integrated over centre-of-mass position vector of two last particles and complemented with isospin variables. The proposed oscillator intrinsic density matrices have a form very suitable for exact realistic density matrix expansion within the framework of Reduced Hamiltonian method. The calculation procedures described above were implemented in computer code. The theoretical formulation have been illustrated by calculation of two-particle oscillator intrinsic density matrices in the case of A=6, E=Emin, and Emin+2. The new computer code for calculation of the two-particle oscillator intrinsic density matrices proves to be very quick, efficient and numerically stable and produces results possessing only small numerical uncertainties